6000 in LEO is not many.
There is a lot of space in space, e.g. the circumference of the equator is 25,000 miles/40,000km and Starlink obviously doesn't travel only around the equator but spreads across the globe - Starlink is in 24 orbital planes, so 6000 satellites in 24 planes is 250 satellites per orbital plane (or in a sense, it's 250 satellites per 40,000km line) and they will all be going in one direction on that plane at the same speed, 160km away from the next one. If there is a problem with one, they can deorbit it within weeks, even if one completely malfunctions, it will fall back to earth by itself in a few years.
Alternative constellations to Starlink won't crowd into Starlinks layer, they'll pick a different altitude and have that to themselves, so completely seperate shells/layers. So don't think in 2d terms like a map of the world, it's in 3d and consequently so much bigger. A bakers oven might fit 100 muffins on a shelf, but with 10 shelves it would have space for 1000 muffins (sorry to any and all bakers, it was for illustrative purposes, I dont know how many muffins/oven

).